How to supinate the arm
In actual anatomy, the humerus (upper arm) would naturally rotate about 60-90 degrees, and the remaining 90-120 degrees would be performed at the distal end of the radius/ulna (essentially the wrist). To model this in a blender armature, I would rotate the upper arm bone ~70 degrees, and the forearm bone ~110 degrees.

Of course, this may introduce problems with skinning. You may want to break your upper and lower arms into 2 or 3 sub-bones each, with constraints that keep them from doing anything other than an axial rotation with respect to each other. Then you can weight paint the surrounding mesh in a gradual fashion so the mesh smoothly rotates just like in reality.